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Title:  Automated trajectory planning for multipleflyby interplanetary missions 
Author(s):  Englander, Jacob 
Director of Research:  Conway, Bruce A. 
Doctoral Committee Chair(s):  Conway, Bruce A. 
Doctoral Committee Member(s):  Prussing, John E.; Coverstone, Victoria L.; Hirani, Anil N. 
Department / Program:  Aerospace Engineering 
Discipline:  Aerospace Engineering 
Degree Granting Institution:  University of Illinois at UrbanaChampaign 
Degree:  Ph.D. 
Genre:  Dissertation 
Subject(s):  optimization
trajectory interplanetary orbital mechanics ceestial mechanics hybrid optimal control mission planning 
Abstract:  Many space mission planning problems may be formulated as hybrid optimal control problems (HOCP), i.e. problems that include both realvalued variables and categorical variables. In interplanetary trajectory design problems the categorical variables will typically specify the sequence of planets at which to perform flybys, and the realvalued variables will represent the launch date, flight times between planets, magnitudes and directions of thrust, flyby altitudes, etc. The contribution of this work is a framework for the autonomous optimization of multipleflyby interplanetary trajectories. The trajectory design problem is converted into a HOCP with two nested loops: an ``outerloop'' that finds the sequence of flybys and an ``innerloop'' that optimizes the trajectory for each candidate flyby sequence. The problem of choosing a sequence of flybys is posed as an integer programming problem and solved using a genetic algorithm (GA). This is an especially difficult problem to solve because GAs normally operate on a fixedlength set of decision variables. Since in interplanetary trajectory design the number of flyby maneuvers is not known a priori, it was necessary to devise a method of parameterizing the problem such that the GA can evolve a variablelength sequence of flybys. A novel ``null gene'' transcription was developed to meet this need. Then, for each candidate sequence of flybys, a trajectory must be found that visits each of the flyby targets and arrives at the final destination while optimizing some cost metric, such as minimizing Δv or maximizing the final mass of the spacecraft. Three different classes of trajectory are described in this work, each of which required a different physical model and optimization method. The choice of a trajectory model and optimization method is especially challenging because of the nature of the hybrid optimal control problem. Because the trajectory optimization problem is generated in real time by the outerloop, the innerloop optimization algorithm cannot require any a priori information and must always return a solution. In addition, the upper and lower bounds on each decision variable cannot be chosen a priori by the user because the user has no way to know what problem will be solved. Instead a method of choosing upper and lower bounds via a set of simple rules was developed and used for all three types of trajectory optimization problem. Many optimization algorithms were tested and discarded until suitable algorithms were found for each type of trajectory. The first class of trajectories use chemical propulsion and may only apply a Δv at the periapse of each flyby. These Multiple Gravity Assist (MGA) trajectories are optimized using a cooperative algorithm of Differential Evolution (DE) and Particle Swarm Optimization (PSO). The second class of trajectories, known as Multiple Gravity Assist with one Deep Space Maneuver (MGADSM), also use chemical propulsion but instead of maneuvering at the periapse of each flyby as in the MGA case a maneuver is applied at a free point along each planettoplanet arc, i.e. there is one maneuver for each pair of flybys. MGADSM trajectories are parameterized by more variables than MGA trajectories, and so the cooperative algorithm of DE and PSO that was used to optimize MGA trajectories was found to be less effective when applied to MGADSM. Instead, either PSO or DE alone were found to be more effective. The third class of trajectories addressed in this work are those using continuousthrust propulsion. Continuousthrust trajectory optimization problems are more challenging than impulsivethrust problems because the control variables are a continuous time series rather than a small set of parameters and because the spacecraft does not follow a conic section trajectory, leading to a large number of nonlinear constraints that must be satisfied to ensure that the spacecraft obeys the equations of motion. Many models and optimization algorithms were applied including direct transcription with nonlinear programming (DTNLP), the inversepolynomial shapebased method, and feasible region analysis. However the only physical model and optimization method that proved reliable enough were the SimsFlanagan transcription coupled with a nonlinear programming solver and the monotonic basin hopping (MBH) global search heuristic. The methods developed here are demonstrated to optimize a set of example trajectories, including a recreation of the Cassini mission, a Galileolike mission, and conceptual continuousthrust missions to Jupiter, Mercury, and Uranus. 
Issue Date:  20130524 
URI:  http://hdl.handle.net/2142/44367 
Rights Information:  Copyright 2013 Jacob Englander. All rights reserved. 
Date Available in IDEALS:  20130524 
Date Deposited:  201305 
This item appears in the following Collection(s)

Dissertations and Theses  Aerospace Engineering

Graduate Dissertations and Theses at Illinois
Graduate Theses and Dissertations at Illinois